how many ordered pairs (a,b), where a,b, are subsets of {1, 2, 3, 4, 5} have aub = {1, 2, 3, 4, 5}
Answers
There are 33,584,224 ordered pairs (a,b) of subsets of {1, 2, 3, 4, 5} such that a ∪ b = {1, 2, 3, 4, 5}.
Let's count the number of ordered pairs (A,B) of subsets of {1, 2, 3, 4, 5} that have A ∪ B = {1, 2, 3, 4, 5}.
First, notice that every element in {1, 2, 3, 4, 5} must be either in A, in B, or in both A and B. Let's count the number of possibilities for each case:
If an element is in A, then it can be one of the 2^5 possible subsets of {1, 2, 3, 4, 5} (since any subset of {1, 2, 3, 4, 5} can be A if we choose the right elements).
This means there are 2^5 possible choices for each of the 5 elements in {1, 2, 3, 4, 5},
for a total of 2^5 * 2^5 * 2^5 * 2^5 * 2^5 = 2^25 possible choices for (A,B) where every element in {1, 2, 3, 4, 5} is in A.
If an element is in B but not in A, then it must be one of the 2^5 - 2 possible subsets of {1, 2, 3, 4, 5} (since it can't be the empty set or {1, 2, 3, 4, 5}).
This means there are 2^5 - 2 possible choices for each of the 5 elements in {1, 2, 3, 4, 5}, for a total of (2^5 - 2)^5 possible choices for (A,B) where some elements are in B but not in A.
If an element is not in A or B, then it must be left out of both A and B. This means there is only one possible choice for each of the 5 elements in {1, 2, 3, 4, 5}, for a total of 1^5 = 1 possible choice for (A,B) where some elements are left out of both sets.
Therefore, the total number of ordered pairs (A,B) of subsets of {1, 2, 3, 4, 5} that have A ∪ B = {1, 2, 3, 4, 5} is:
2^25 + (2^5 - 2)^5 + 1 = 33554432 + 29791 + 1 = 33584224
So there are 33,584,224 ordered pairs (a,b) of subsets of {1, 2, 3, 4, 5} such that a ∪ b = {1, 2, 3, 4, 5}.
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Related Questions
what is 29/5 is equal to
Answers
Answer:
5 4/5 or 5.8
Step-by-step explanation:
convert 29/5 to 5 4/5
or
divide 29/5 is 5.8
Given the equation 15 equals y over -4, solve for y.
Answers
Answer:
y=60
Step-by-step explanation:
\(15=\frac{y}{-4} \\(15)*-4=(\frac{y}{-4} )*-4\\-240=y\)
WILL GIVE BRAINLIEST IF YOU HELP MEE
Answers
Answer: A: Whole Number B:Integer and C: Rational are all correct.
For the question: In the figure, AB is divided into equal parts. The coordinates of point A are (2, 4), and the coordinates of point B are (10, 6). Match each pair of coordinates to the corresponding point on AB.
Answer:The coordinates of the point are (6 , 5).
For the question: Imani and Abedi drive to work. Imani drives 66 miles in 1.5 hours. Abedi drives 56 km in 1 hour 15 min. Work out the difference between their average speeds in km/h. 1 mile = 1.6 km
Answer:25.6 km/h
I couldn't help you on all of them, but I helped you on some. Hope this helps :D
what is the point-slope form of a line with slope -4 that contains the point (-2, 3)
Answers
Answer:
\(y - 3 = - 4(x + 2)\)
Graph g(x)=−|x+3|−2 dude i absolutely hate graphing. Does anyone else do summer school algebra on keystone.? (Also i need help please)
Answers
Answer:
Graph using graphing calc or desmos.
Step-by-step explanation:
Answer:
your graph is below. i have algebra 2 on flvs.
A paint store sells an orange paint that is made by combining 7 parts red with 4 parts
yellow. A customer tried to recreate the order at home, but made a mistake. Her
container has 4 parts red paint and 8 parts yellow paint. How much red paint does she
need to add to get the correct shade of orange?
Answers
Answer:
10 parts red paint
Step-by-step explanation:
she doubled the amount of yellow paint in the can at home, so you will need to add twice the amount of red paint. 7×2=14, 14-4= 10.
Which one of the following would be most helpful in strengthening the content validity of a test?
A. Administering a new test and an established test to the same group of students.
B. Calculating the correlation coefficient.
C. Calculating the reliability index.
D. Asking subject matter experts to rate each item in a test.
Answers
Asking subject matter experts to rate each item in a test would be most helpful in strengthening the content validity of a test
Asking subject matter experts to rate each item in a test would be most helpful in strengthening the content validity of a test. Content validity refers to the extent to which a test accurately measures the specific content or domain it is intended to assess. By involving subject matter experts, who are knowledgeable and experienced in the domain being tested, in the evaluation of each test item, we can gather expert opinions on the relevance, representativeness, and alignment of the items with the intended content. Their input can help ensure that the items are appropriate and adequately cover the content area being assessed, thus enhancing the content validity of the test.
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Write the prime factorization of 21. Use exponents when appropriate and order the factors from least to greatest (for example, 2235).
Answers
The prime factorization of the number 21 is:
21 = 3*7
How to write the prime factorization?We want to write the prime factorization of 21.
To do so, we just need to divide the number by prime numbers.
The first prime number we can try is 2, if we divide by 2 we get:
21/2 = 10.5
This is not an integer, so 2 is not a factor.
The next one is 3:
21/3 = 7
Now we can rewrite:
21 = 3*7
Where 3 and 7 are prime numbers, so that is the prime factorization.
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3.
Which statement about the number 7,777 is true?
A. There is a 7 in the tens place, so 7 times 10 equals 700.
B. There is a 7 in the hundreds place, so 7 times 100 equals 70.
C. There is a 7 in the tens place, so 7 times 10 equals 70.
D. There is a 7 in the thousands place, so. 7 times 1,000 equals 700.
Answers
Answer:
C. There is a 7 in the tens place, so 7 times 10 equals 70.
Math question I need help with it please help me !
Answers
Answer:
96 degrees
Step-by-step explanation:
Answer:
x = 5°
Step-by-step explanation:
Because of the given congruency,
Angle A = Angle D = 50° = 10x
10x = 50
x = 5°
HOPE IT HELPS!!!
The base of a parallelogram is six more than twice the height. The height is 5 inches. What is the length of the base?
Answers
The length of the base of the parallelogram is 16 inches.
What is parallelogram?
A parallelogram is a four-sided plane figure with opposite sides parallel and congruent (having the same length). This means that the opposite sides of a parallelogram are parallel to each other and have the same length. Additionally, the opposite angles of a parallelogram are equal in measure, which means they have the same degree of rotation.
Let's use the information given in the problem to set up an equation and solve for the length of the base.
From the problem, we know that the height of the parallelogram is 5 inches.
h = 5
We also know that the base of the parallelogram is six more than twice the height. Let's use b to represent the length of the base:
b = 2h + 6
Now we can substitute the value we know for the height and solve for the base:
b = 2(5) + 6
b = 10 + 6
b = 16
Therefore, the length of the base of the parallelogram is 16 inches.
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help please !!!! Please !!!!
Answers
Answer:
child byeee kid jdhuwkjikw
Step-by-step explanation:
‼️WILL MARK BRAINLIEST‼️
Answers
The average distance of electric cars is 275.
The range of the data set is 300.
How to solveGiven:
Average of the data set = 275Range of the data set = 300To find: Average distance of electric cars
Solution:
The average distance of electric cars can be calculated by finding the average of the data set containing the distances of electric cars. Let's assume that the data set is as follows:
250, 250, 250, 400, 300, 300, 350, 100
To find the average distance of electric cars, we can use the formula:
Average = (Sum of all the data points) / (Number of data points)
Substituting the given values, we get:
Average = (250 + 250 + 250 + 400 + 300 + 300 + 350 + 100) / 8
Average = 2200 / 8
Average = 275
Therefore, the average distance of electric cars is 275.
Now, let's calculate the range of the data set. The range is the difference between the maximum and minimum values in the data set. From the given data set, we can see that the minimum value is 100 and the maximum value is 400.
Range = Maximum value - Minimum value
Range = 400 - 100
Range = 300
Therefore, the range of the data set is 300.
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The inverse demand curve a monopoly faces is \[ p=15 Q^{-0.5} \text {. } \] What is the firm's marginal revenue curve? Marginal revenue (MR) is \( \mathrm{MR}=\quad \) (Properly format your expression
Answers
The firm's marginal revenue (MR) curve can be derived by taking the derivative of the inverse demand curve with respect to quantity (Q). In this case, the inverse demand curve is given by p=15Q^−0.5.
.To find the marginal revenue, we differentiate the inverse demand curve with respect to Q.The negative sign in the marginal revenue curve arises because the inverse demand curve is downward sloping. The marginal revenue curve represents the change in total revenue resulting from selling one additional unit of output. In this case, the marginal revenue curve is a power function with a negative exponent. As quantity (Q) increases, the marginal revenue decreases, reflecting the fact that the firm must lower the price to sell more units. The marginal revenue curve intersects the quantity axis at a positive value, indicating that marginal revenue is positive when the quantity is low. However, as quantity increases, marginal revenue becomes negative, indicating that each additional unit sold contributes less to total revenue
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given that the probability of a student spending time watching tv is 0.89, and the probability of a student spending time reading and watching tv is 0.11, what is the probability of a student spending time reading given that the student spends time watching tv? be sure to round your answer to two significant digits.
Answers
The probability of a student spending time reading given that the student spends time watching TV is \(P(Reading|Watching\:\:TV)=0.12\)
If any two occurrences in sample space S, A and B, are specified, then the conditional probability of event A given B is:
\(P(A|B)=\frac{P(A\:and\:B)}{P(B)}\)
Probability theory is an important branch of mathematics that is used to model and analyze uncertain events in various fields, including science, engineering, finance, and social sciences. The concept of probability is based on the idea of random experiments, where the outcomes are uncertain and can vary each time the experiment is performed.
The probability of an event can be determined by analyzing the possible outcomes of the experiment and assigning a probability to each outcome based on the assumptions of the model. The theory of probability has several applications in real life, such as predicting the outcomes of games of chance, evaluating risks in insurance and finance, and making decisions in scientific research.
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Adwoa received a commission of 20% on bread she sold. In one week her commission was GH$540
Answers
The total sales made by Adwoa in one week was GH₵ 2700. Answer: GH₵ 2700
The given statement can be written in mathematical notation as, 20/100 × x = 540 where x is the total sales made in a week by Adwoa. We need to calculate the total sales made by Adwoa in a week.
Let’s solve the above equation to determine x.20/100 × x = 540 Dividing both sides by 20/100.x = 540 ÷ 20/100.x = 540 × 100/20x = 2700GHS
Therefore, the total sales made by Adwoa in one week was GH₵ 2700. Answer: GH₵ 2700
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please it do in 6 min i need help with this one please The following points are from a dilation. If
B(0 , 5 ) and B'(x, 2 0 ), what is x?
Answers
Answer:
The value of x = 0
Step-by-step explanation:
Given
B(0, 5)B'(x, 20)To determine
The value of x = ?
If we closely observe the value of the y-coordinate of the image B'(x, 20), we can see that the y-coordinate of the image B' is 4 times the y-coordinate of the original point (0, 5).
i.e. y → 5×4 =20
It means the coordinates of the image B'(x, 20) can be determined by dilating the original point (0, 5) by a scale factor of 4.
Thus, the x-coordinate of B'(x, 20) can also be obtained by multiplying the x-coordinate of B(0, 5) by 4.
i.e. x → 4×0 = 0
Thus, the rule of dilation is:
P(x, y) = P'(4x, 4y)
Hence,
B(0, 5) → B'(4(0), 4(5)) → B'(0, 20)
Thus,
The value of x = 0 ∵ 0×4 = 0
Which transformations will change Figure A into Figure B?
rotate 180° about the origin, dilate by a scale
factor of
rotate 180° about the origin, dilate bya scale
factor of
A
reflect over the line y = , dilate bya scale
factor of
reflect over the line y = T, dilate by a scale
factor of
Answers
Answer:
the second answer should be correct
Step-by-step explanation:
:)
Answer:
second option
Step-by-step explanation:
hejabwdychbdscuadsva,syjdh help.
Answers
You add 3 to -6 and add 1 to 3 to get -3,4
If one pan takes 12 cupcakes, how many batches will she have to bake for
105 cupcakes?
Answers
Answer: 9
Step-by-step explanation: 105/12=8.75
8 batches are not enough so she should do it one more time to finish
If n(Ax B) = 72 and n(A) = 24, find n(B).
Answers
Solving for Cartesian product n(B), we have n(B) = 72 / 24 = 3.
What is Cartesian product?The Cartesian product is a mathematical operation that takes two sets and produces a set of all possible ordered pairs of elements from both sets.
In other words, if A and B are two sets, their Cartesian product (written as A × B) is the set of all possible ordered pairs (a, b) where a is an element of A and b is an element of B.
For example, if A = {1, 2} and B = {3, 4}, then A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}.
By the question.
We know that n (Ax B) represents the number of elements in the set obtained by taking the Cartesian product of sets A and B.
Using the formula for the size of the Cartesian product, we have:
n (Ax B) = n(A) x n(B)
Substituting the given values, we get: 72 = 24 x n(B)
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Select the best answer regarding the effects of Carbon monoxide: a. The affinity between CO and hemoglobin is about the same as oxygen. b. The central chemoreceptors will detect the reduction in oxygen delivered to the cells and will increase their firing rate. c. CO results in less oxygen loading hemoglobin but unloading is not changed. d. A small amount of CO in the air will not reduce arterial PO2 levels enough to be sensed by the peripheral chemoreceptors.
Answers
The best answer regarding the effects of carbon monoxide is option c, CO results in less oxygen loading hemoglobin but unloading is not changed.
Carbon monoxide binds up more tightly to the hemoglobin as compared to the oxygen molecules. This reduces the oxygen-carrying capacity of the blood and results in less oxygen loading onto hemoglobin.
However, once oxygen is already bound to hemoglobin, CO does not significantly affect its release or unloading. Therefore, option c is the most accurate statement among the given choices.
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Blake has a total of 11,000 to invest in two accounts. one account earns 4% simple interest, and the other earns 5% simple interest. how much should be invested in each account to earn exactly $490 at the end of 1 year?
Answers
Blake should invest $6,000 at 4% interest and the remaining $5,000 (11000 - 6000) at 5% interest to earn exactly $490 at the end of 1 year.
Let's denote the amount of money Blake invests at 4% interest as "x" (in dollars) and the amount he invests at 5% interest as "11000 - x" (since the total investment is $11,000).
To earn interest, we can use the formula: Interest = Principal × Rate × Time
For the 4% interest account, the interest earned is:
0.04x × 1 (1 year) = 0.04x
For the 5% interest account, the interest earned is:
0.05(11000 - x) × 1 (1 year) = 550 - 0.05x
According to the problem, the total interest earned is $490. Therefore, we can set up the equation:
0.04x + (550 - 0.05x) = 490
Simplifying the equation:
0.04x + 550 - 0.05x = 490
-0.01x + 550 = 490
-0.01x = -60
x = 6000
Blake should invest $6,000 at 4% interest and the remaining $5,000 (11000 - 6000) at 5% interest to earn exactly $490 at the end of 1 year.
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One week Christopher earned $404.80 at his job when he worked for 22 hours if he’s paid the same hourly wage how many hours would he have to work the next week to earn $368
Answers
It will take 20 hours for Christopher to earn $368
Christopher earns $404.80 for 22 hours, the amount he will earn in one hour can be calculated as follows
404.80= 22
x= 1 hour
cross multiply both sides
22x= 404.80
x= 404.80/22
x= 18.4
He will earn $18.4 in one hour
The number of hours he will have to work for $368 can be calculated as follows
= 368/18.4
= 20
Hence Christopher will have to work for 20 hours
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The number of hours Christopher has to achieve to earn weekly wages of $368 next week is 20
What is the total wages?
The total wages can be determined as the hourly rate multiplied by the number of working hours in a week
weekly wages=hourly rate*number of hours
weekly wages=$404.80
hourly rate=unknown=assume it is R
number of hours worked=22
$404.80=R*22
R=$404.80/22
R=$18.40
The number of work hours that needs to be achieved to earn $368 next week is determined in a similar manner where number of hours is the unknown(H)
$368=$18.40*H
H=$368/$18.40
H=20
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Use the rule y = -x + 7 to fill in the blank. If (-1, y) is on the graph, then y=
I will give brainiest
Answers
Answer:
if y = -x +7
therefore y =-1 +7 = 6
(-1,6) y =6
1.) Expand [5x-2]³ Please I marking brainliest for Remarkable answers
Answers
Answer:
125x³ - 150x² + 60x - 8
Step-by-step explanation:
Method 1
Expand the brackets using the FOIL method:
\(\begin{aligned}(5x-2)^3&=(5x-2)(5x-2)(5x-2)\\&=(25x^2-10x-10x+4)(5x-2)\\&=(25x^2-20x+4)(5x-2)\\&=125x^3-50x^2-100x^2+40x+20x-8\\&=125x^3-150x^2+60x-8\end{aligned}\)
Method 2
Apply the Perfect Cube Formula
\(\boxed{\begin{minipage}{5 cm}\underline{Perfect Cube Formula}\\\\$(a-b)^3=a^3-3a^2b+3ab^2-b^3$\\\end{minipage}}\)
\(\begin{aligned}(5x-2)^3&=(5x)^3-3 \cdot (5x)^2 \cdot 2+3 \cdot 5x \cdot 2^2-2^3\\&=5^3 \cdot x^3-6 \cdot 5^2 \cdot x^2+3 \cdot 5x \cdot 4-8\\&=125x^3-6 \cdot 25x^2+12 \cdot 5x-8\\&=125x^3-150x^2+60x-8\end{aligned}\)
A piece of copy paper is about 0.004 inches. What is 0.004 inches written in
scientific notation?
A 4 x 10-4
B 4 x 10-3
C 4 x 104
D 4 x 103
Answers
Answer:
B
Step-by-step explanation:
If the direction of the decimal point is going to the right, the exponent is negative.
Basically the other guys explanation is what the explanation is
How do you do this- it’s homework
Answers
Answer:
n = 12
Step-by-step explanation:
I assume in problem 4 the relation between miles and hours is proportional.
Set up a proportion.
45 miles is to 4 hours as 135 miles is to n hours.
45/4 = 135/n
Cross multiply.
45n = 4 × 135
n = 4 × 3
n = 12
Answer:
12
Step-by-step explanation:
Because we can divide 45 and 4 and we get 11.25
Now we know that one hour is 11.25 miles. So just divide 135/11.25
and you get 12
im pretty sure thats the correct answer. Hope this helps
find the distance between the points (-16,11) and (16,4)
Answers
\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-16}~,~\stackrel{y_1}{11})\qquad (\stackrel{x_2}{16}~,~\stackrel{y_2}{4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~16 - (-16)~~)^2 + (~~4 - 11~~)^2} \implies d=\sqrt{(16 +16)^2 + (4 -11)^2} \\\\\\ d=\sqrt{( 32 )^2 + ( -7 )^2} \implies d=\sqrt{ 1024 + 49 } \implies d=\sqrt{ 1073 }\implies d\approx 32.76\)
pls help i will give u brainliest!! ^_^
Answers
Please mark me as brainliest.
Hope this helps!!